What factors determine a protein's rate of evolution are actively debated. Especially unclear is the relative role of intrinsic factors of present-day proteins versus historical factors such as protein age. Here we study the interplay of structural properties and evolutionary age, as determinants of protein evolutionary rate. We use a large set of one-to-one orthologs between human and mouse proteins, with mapped PDB structures. We report that previously observed structural correlations also hold within each age group - including relationships between solvent accessibility, designabililty, and evolutionary rates. However, age also plays a crucial role: age modulates the relationship between solvent accessibility and rate. Additionally, younger proteins, despite being less designable, tend to evolve faster than older proteins. We show that previously reported relationships between age and rate cannot be explained by structural biases among age groups. Finally, we introduce a knowledge-based potential function to study the stability of proteins through large-scale computation. We find that older proteins are more stable for their native structure, and more robust to mutations, than younger ones. Our results underscore that several determinants, both intrinsic and historical, can interact to determine rates of protein evolution.